For each nge1, let fn:[0,1]tomathbb R be defined as fn(x)=begincasesnx&if xin[0,tfrac1n], 2-nx&if xin(tfrac1n,tfrac2n], 0&if xin(tfrac2n,1].endcases Which of the following statements is true?

(C) (fn)nge1 converges pointwise on [0,1] to a continuous function f.

Q26Section B (Part B)26 of 120

Pointwise limit of tent functions

For each $n\ge1$ , let $f_n:[0,1]\to\mathbb R$ be defined as

$f_n(x)=\begin{cases}nx&\text{if }x\in\big[0,\tfrac1n\big],\ 2-nx&\text{if }x\in\big(\tfrac1n,\tfrac2n\big],\ 0&\text{if }x\in\big(\tfrac2n,1\big].\end{cases}$

Which of the following statements is true?

Pick an option to check your answer.

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